Waverly's mother is a very proud and strong woman who tries to achieve recongnition through her dauther's accomplishments in chess and when Waverly gains national recognition her mother starts making Waverly's victories hers.
There is nothing wrong with a mother being proud of her daugther's triumphs, but in the case of Waverly her mother became obsessed with her daugther at the point of trying to live her life through Waverly. And the worring part is that all this was covered under the mask of love, Waverly's mother never meant any harm for her daughter, all the damaged she caused was disguised by love, and this is where the phrase "A parent’s love can be described as a double-edged sword, having the power to both defend and destroy a child" becomes valid, sometimes love can do more damage because when you see it you can not protect yourself, it is love in the end.